Super Efimov effect for mass-imbalanced systems

TL;DR

This paper demonstrates the existence of the super Efimov effect in a two-dimensional mass-imbalanced two-species system with p-wave resonance, revealing an infinite tower of bound states with doubly exponential energy scaling.

Contribution

It introduces a low-energy effective field theory analysis showing the super Efimov effect occurs for specific mass ratios in 2D systems, which was not previously established.

Findings

Super Efimov states appear when mass ratio exceeds critical values.

The spectrum density increases with higher mass ratios, aiding experimental detection.

Born-Oppenheimer approximation fails to predict the super Efimov effect.

Abstract

We study two species of particles in two dimensions interacting by isotropic short-range potentials with the interspecies potential fine-tuned to a p-wave resonance. Their universal low-energy physics can be extracted by analyzing a properly constructed low-energy effective field theory with the renormalization group method. Consequently, a three-body system consisting of two particles of one species and one of the other is shown to exhibit the super Efimov effect, the emergence of an infinite tower of three-body bound states with orbital angular momentum $l=\pm1$ whose binding energies obey a doubly exponential scaling, when the two particles are heavier than the other by a mass ratio greater than 4.03404 for identical bosons and 2.41421 for identical fermions. With increasing the mass ratio, the super Efimov spectrum becomes denser which would make its experimental observation easier. We also point out that the Born-Oppenheimer approximation is incapable of reproducing the super Efimov effect, the universal low-energy asymptotic scaling of the spectrum.